This is the 347th most frequent Persian word.
کردهاند
"Have done" or "they have done."
In this sentence, 'کردهاند' follows 'تصمیم' (decision), forming 'تصمیم کردهاند' (have decided), denoting the completion of the act of deciding.
آنها تصمیم گرفتهاند که به مسافرت بروند.
They have decided to go on a trip.
The term 'کردهاند' in 'منتشر کردهاند' (have published) indicates the completion of the act of publishing.
کتابهای زیادی منتشر کردهاند.
They have published many books.
Here, 'کردهاند' is not directly used; however, its conjugation '-اند' applies to a verb, indicating completed action ('نشان دادهاند' = 'have shown').